A simple interpretation of undirected edges in essential graphs is wrong

Area of Science:

• Causal inference
• Machine learning
• Graph theory

Background:

• Markov equivalence classes of directed acyclic graphs (essential graphs) are used in AI for causal discovery.
• Uncertainty in causal directionality is represented by undirected edges in essential graphs.
• Existing interpretations of undirected edges lack a robust framework for quantifying causal uncertainty.

Purpose of the Study:

• To address the ambiguity in interpreting undirected edges within essential graphs.
• To identify and rectify flawed interpretations that lead to betting paradoxes (Dutch books).
• To propose and validate a new interpretation for undirected edges that ensures betting consistency.

Main Methods:

• Demonstration of the vulnerability of the simple interpretation to Dutch booking.
• Development and proof of a new interpretation for undirected edges.
• Analysis of edge orientation likelihoods in small causal graphs (4 nodes, 3 edges).

Main Results:

• The simple interpretation of undirected edges as equally likely orientations is susceptible to Dutch books.
• A novel interpretation is proposed and proven to prevent such betting paradoxes.
• Undirected edges with directional bias are prevalent in small causal graphs.

Conclusions:

• A more rigorous interpretation of undirected edges is crucial for reliable causal discovery.
• The proposed interpretation provides a sound strategy for handling causal uncertainty.
• Understanding edge orientation likelihoods is important for practical causal inference applications.